MHT CET · Physics · Electrostatics
Surface density of charge on a charged conducting sphere of radius 'R' in terms of electric intensity 'E' at a distance 'r' in free space is \(\left(\mathrm{r}>\mathrm{R}, \mathrm{E}_{0}=\right.\) permittivity of free space \()\)
- A \(_{1} \in_{0} E \frac{R}{r}\)
- B \(v^{2} \in_{0} E\left(\frac{r}{R}\right)^{2}\)
- C \(x_{3} \in_{0} E \frac{r}{R}\)
- D \(x^{4} \in_{0} E\left(\frac{R}{r}\right)^{2}\)
Answer & Solution
Correct Answer
(B) \(v^{2} \in_{0} E\left(\frac{r}{R}\right)^{2}\)
Step-by-step Solution
Detailed explanation
\(E=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \frac{4 \pi R^{2} \sigma}{r^{2}}=\frac{\sigma R^{2}}{\varepsilon_{0} r^{2}}\)
\(\therefore \sigma=E \varepsilon_{0}\left(\frac{r}{R}\right)^{2}\)
\(\therefore \sigma=E \varepsilon_{0}\left(\frac{r}{R}\right)^{2}\)
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